Question

What is the equation of the line between `(-9,16)` and `(-4,12)`?

Answer 1

`(-9,16)` and `(-4,12)`

Let's use the point-slope formula

`(y_2-y_1)/(x_2-x_1)`

`(12-16)/(-4--9)`

`(color(green)(-4))/color(blue)(5`

Now we have the slope for point-slope form, which is `y =mx+b` with `m` being the slope and `b` as the `y`-intercept, the value of `x` when `y=0`

Let's guess:

`y=-4/5x+5`
graph{y=-4/5x+5}

Were looking for `(-4, 12)`

Nope, not quite

`y=-4/5x+5.2`
graph{y=-4/5x+5.2}

Almost

`y=-4/5x+7.8`
graph{y=-4/5x+7.8}

We're so close

`y=-4/5x+8.8`
graph{y=-4/5x+8.8}

Great! We have our equation!

`y=-4/5x+8.8`